Math and Art: The Art of the Ellipse
The author gives a nice, if long, explanation about the significance of the ellipse, but it basically boils down to this: circles are everywhere. And often, when we are looking at circles, we’re looking at them atilt. We see projections of the circle, and projections of circles are ellipses.
Think of it this way: suppose you have a hula hoop and you hold it parallel to the ground. The shadow you see is circular, but if you tilt the hula hoop, the shadow will change–into an ellipse. I don’t have a hula hoop, so I made do with a spare key ring:
As the circular key ring is rotated, it becomes less parallel to the ground; the shadow becomes less circular and more elliptical. And at the end, the ellipse vanishes–an ellipse eclipse!